The following figure shows the normal distribution with the proportion of the ar

Question

The following figure shows the normal distribution with the proportion of the area under the normal curve contained within one, two, and three standard deviations of the mean. The last proportion on each side, 0.13%, depicts the remaining area under the curve. Specifically, 0.13% of the area under the standard normal distribution is located above z-score values greater than the mean (mu) plus three standard deviations (+3 sigma). Also, because the normal distribution is symmetrical, 0.13% of the area under the standard normal distribution is located below z-score values less than the mean (mu) minus three standard deviations (-3 sigma). Use the figure to help you answer the following questions. The National Assessment of Educational Progress (NAEP) is a nationwide assessment of students' proficiency in nine subjects: mathematics, reading, the civics, geography, and us. history. The main NAEP assessments are conducted annually on of students from grades 4, 8, and 12. In 2000, the science scores for female students had a mean of with a standard deviation of 35. Assume that these scores are normally distributed with the given mean and standard deviation. A score of 111 is ______below the mean, while a score of 181 is ______ above the mean. This means that the percentage of female students with scores between 111 and 181 is _______

Explanation / Answer

A score of 111 is 34.13%(one standard deviation) below the mean while a score of 181 is 34.13%(one standard deviation) above the mean . this means that the percentage of female students scores between 111 and 181 is 68.26%.

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